Components with strictly controlled access to the services and/or to the data typically have an architecture formed around the microprocessor and a program memory including the secret key. Such components are used for example in smart cards, especially for banking applications, via a control terminal or remote terminal. Such components use one or more secret key encryption or private key encryption methods to compute an output data from an input data. Such a method is used for example to encipher, decipher, authenticate or sign an input message or else verify the signature of the input message.
To ensure the security of the transactions, the secret key or private key encryption methods are constructed in such a way that it is not possible to determine the secret key used from the knowledge of the input data and/or the output data of the algorithm. However, the security of a component relies on its capacity to keep the secret key that it uses concealed, for this key cannot be modified.
One method frequently used is the DES (Data Encryption Standard) type method. This method can be used for example to give an enciphered message MS (or output data) encoded on 64 bits, from a plaintext message ME (or input data) also encoded on 64 bits, and a secret 56-bit key K0. The main steps of the DES are described in detail with reference to FIG. 1. After an initial permutation IP, the block formed by the permutated bits of the input data is separated into a left-hand part L0 and a right-hand part R0.
After this, 16 rounds of identical operations are performed. During each round of operations, the right-hand part (R0, . . . , R15) of an intermediate data computed during the previous round of operations is combined with a derivative key (M1, . . . , M16) during a transformation called a transformation F. The result of the transformation F is then added (XOR operation) to the left-hand part (L0, . . . , L15) of the intermediate data computed during the previous round of operations.
After the 16th round of operations, the left-hand part L16 and right-hand part R16 of the 16th intermediate data are assembled and a final permutation IP−1, which is the inverse of the initial permutation IP, terminates the procedure. An i-ranking round of operations included between 1 and 16 is described in detail with reference to FIG. 2. The 56 bits of an intermediate key Ki−1 computed during the previous round are shifted (operation Si) to give a new updated intermediate key Ki, then 48 bits out of 56 are selected by an operation PC of permutation/compression to provide a derived key Mi−Mi=PC(Ki)=PC(Si(Ki−1). The association of the steps PC and Si forms a key computation step ET2.
In parallel, the transformation F is carried out. The right-hand part Ri−1 of a piece of intermediate data computed during the previous round is extended to 48 bits by an expansion (operation E), combined with the derived key M by an XOR type operation, replaced by 32 new bits by a substitution operation (represented by the operation SBOX), then permutated once again (operation P). In practice, the operations F, P, E, PC, SBOX are identical for all the rounds. On the contrary, the operations S1 to S16 used during the computation of the derived keys K1 to K16 are different from one round to another.
All the characteristics of the operations IP, Ip−1, P, PC, E, SBOX, Si performed during the implementation of a DES method are known: the computations made, the parameters used, etc. These characteristics are, for example, described in detail in the patent application WO 00/46953 or in the “Data Encryption Standard, FIPS PUB 46”, published on 15 Jan. 1977.
The security of a component using an secret key or private key encryption method lies in its capacity to keep the key that it uses secret, especially when it undergoes SPA type analysis. In an SPA analysis, the component is made to execute several time the encryption method that it uses by applying the same input data ME, and, for each execution of the method, the trace left by this execution is measured as a function of time. The trace represents, for example, the power consumption of the component or the electromagnetic energy radiated as a function of time. The set of measurements are then averaged to eliminate the noise from the measurement and obtain the real trace of the circuit for a fixed input data ME. For example, a set of 10 to 1000 identical measurements may be enough to eliminate the noise from the measurement and obtain the real trace of the component for a fixed input data ME.
The form taken by a trace such as this is shown in FIG. 3, in the case of a DES type method. This figure clearly shows the different steps of the DES method: initial permutation IP before the instant t1, 16 rounds of operation between the instant t2 and t1, t3 and t2, . . . , t17 and t16, and final permutation IP−1 after the instant t17. As can be seen in the trace of FIG. 3, it is thus fairly simple to obtain information on the secret key used in the case of a component using a standard DES method. For example, it is possible, for each round of operations, to determine an image of a derived key Mi by identifying the time interval during which a derived key transfer instruction is carried out before the execution of the XOR operation. Since all the derived keys M1 to M16 are obtained from the secret key K0 by known operations, the knowledge of simple images of the derived keys provides information on the secret key.
More generally, all the encryption methods using secret keys are more or less sensitive to SPA type analysis. Their sensitivity is especially important during the performance of a critical step during which the secret key is used either directly or in a derived form obtained by a known law of derived key scheduling. A critical step of this kind is for example a derived key scheduling step during which an updated derived key Mi is computed from a previously computed key Ki−1.